A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side

作者：Dieci Luca; Lopez Luciano^*

来源：Journal of Computational and Applied Mathematics, 2012, 236(16): 3967-3991.

DOI：10.1016/j.cam.2012.02.011

• Discontinuous ODEs
• One-step and multistep methods
• Event driven
• Time-stepping methods

This work work is dedicated to the memory of Donato Trigiante who has been the first teacher of Numerical Analysis of the second author. The authors remember Donato as a generous teacher, always ready to discuss with his students, able to give them profound and interesting suggestions. %26lt;br%26gt;Here, we present a survey of numerical methods for differential systems with discontinuous right hand side. In particular, we will review methods where the discontinuities are detected by using an event so-called event driven methods) and methods where the discontinuities are located by controlling the local errors (so-called time-stepping methods). Particular attention will be devoted to discontinuous systems of Filippov%26apos;s type where sliding behavior on the discontinuity surface is allowed.

• 出版日期2012-10